Dissociable Prior Influences of Signal Probability and Relevance on Visual Contrast Sensitivity

Correction

PSYCHOLOGICAL AND COGNITIVE SCIENCES Correction for “Dissociable prior influences of signal probability and relevance on visual contrast sensitivity,” by Valentin Wyart, Anna Christina Nobre, and Christopher Summerfield, which appeared in issue 9, February 28, 2012, of Proc Natl Acad Sci USA (109:3593–3598; first published February 13, 2012; 10.1073/ pnas.1120118109). The authors note that on page 3597, right column, the third equation (for soft threshold nonlinearity) appeared incorrectly. The corrected equation appears below: x Γ½x ¼ x þ α − exp α

www.pnas.org/cgi/doi/10.1073/pnas.1204601109

6354 | PNAS | April 17, 2012 | vol. 109 | no. 16 www.pnas.org Downloaded by guest on September 30, 2021 Dissociable prior inﬂuences of signal probability and relevance on visual contrast sensitivity

Valentin Wyarta,1, Anna Christina Nobrea,b, and Christopher Summerﬁelda aDepartment of Experimental Psychology, University of Oxford, Oxford OX1 3UD, United Kingdom; and bOxford Centre for Human Brain Activity, Department of Psychiatry, University of Oxford, Warneford Hospital, Oxford OX3 7JX, United Kingdom

Edited by Ranulfo Romo, Universidad Nacional Autonoma de Mexico, Mexico City, DF, Mexico, and approved January 18, 2012 (received for review December 7, 2011) According to signal detection theoretical analyses, visual signals increasing the baseline activity of signal-selective units or by occurring at a cued location are detected more accurately, whereas shifting the observer’s decision criterion toward one of the two frequently occurring ones are reported more often but are not better responses. However, the binary classification of stimuli as signal- − distinguished from noise. However, conventional analyses that present (S+) and signal-absent (S ) used by conventional SDT estimate sensitivity and bias by comparing true- and false-positive analyses makes it difficult to arbitrate between these different rates offer limited insights into the mechanisms responsible for these possibilities, for a number of reasons. First, the conventional ap- effects. Here, we reassessed the prior influences of signal probability proach does not distinguish between the two successive sources and relevance on visual contrast detection using a reverse-correla- of performance-limiting noise in the decision process: external tion technique that quantifies how signal-like fluctuations in noise noise (physical noise in the stimulus itself) and internal noise predict trial-to-trial variability in choice discarded by conventional (physiological noise during stimulus processing). This conflation analyses. This approach allowed us to estimate separately the makes it hard to pinpoint the locus of contextual influences on sensitivity of true and false positives to parametric changes in signal signal detection (e.g., whether effects occur upstream or down- energy. We found that signal probability and relevance both stream from internal noise) (16). Second, the binary classifica- increased energy sensitivity, but in dissociable ways. Cues predicting tion of stimuli does not allow to measure sensitivity separately in − the relevant location increased primarily the sensitivity of true the S+ and S categories. This is important, because different positives by suppressing internal noise during signal processing, mechanisms make distinct predictions as to whether their effects COGNITIVE SCIENCES whereas cues predicting greater signal probability increased both on sensitivity should grow or shrink with signal strength (17). PSYCHOLOGICAL AND the frequency and the sensitivity of false positives by biasing the Reverse-correlation analyses offer a powerful complement to baseline activity of signal-selective units. We interpret these findings conventional analyses, by permitting the measurement of ob- in light of “predictive-coding” models of perception, which propose server sensitivity to small, noise-driven changes in image statistics separable top-down influences of expectation (probability driven) (18, 19). Here we adopted a reverse-correlation approach to and attention (relevance driven) on bottom-up sensory processing. identify the mechanisms by which signal probability and relevance influence signal detection. To do so, we quantified the decision making | psychophysics | visual perception amount of signal energy present in each noisy stimulus by convolution with a pool of visual filters that approximate the re- ignal detection theory (SDT) proposes that sensitivity can be ceptive fields of orientation-selective neurons in early visual Scalculated by comparing true- and false-positive rates (1, 2). In cortex (20, 21). This parametric characterization of external a typical detection task, subjects are asked to judge whether a noisy noise allowed us to estimate the sensitivity of human observers to + − stimulus does or does not contain a low-energy signal, allowing signal-like fluctuations separately in S and S stimuli. In con- researchers to classify stimuli judged as containing the signal into junction with a signal detection task in which two types of cues true and false positives (“hits” and “false alarms,” respectively), provided mutually independent information about probability and stimuli judged as not containing the signal into true and false and relevance, this approach allowed us to dissociate and arbi- negatives (“correct rejections” and “misses”). SDT posits that trate between their candidate mechanisms. d′ performance can be summarized by two statistics: , indexing Results sensitivity to signal occurrence in signal-to-noise units, and c, Probability × Relevance Cueing Procedure. fi reflecting a bias to report signal occurrence (modeled as a decision While xating centrally, subjects viewed two simultaneously presented stimuli in colored criterion). Using this approach, it is now well established that cues fi A that predict the location of a behaviorally relevant signal increase placeholders located in their left and right visual elds (Fig. 1 ). Their task was to report whether a signal was present (S+)or sensitivity (3–6) by improving the precision of visual processing (7– − absent (S ) in one of the two placeholders, indicated by a color- 10). By contrast, cues that predict a greater probability of signal matched probe presented after stimulus offset. The target signal occurrence alone are believed to have no influence on sensitivity was a vertical Gabor pattern of two cycles per degree of visual (11, 12) but instead bias observers to report signal occurrence by angle, presented at a fixed contrast titrated for each subject be- adopting a more liberal decision criterion. fore the experiment. All stimuli were embedded in visual noise Over the past 50 years, SDT has provided a versatile de- whose frequency characteristics closely matched those of the scription of decision processes, both in laboratory experiments signal (Methods). We manipulated signal probability at the block and in real-world situations such as medical diagnostics, by dis- sociating between an observer’s sensitivity and bias, two quanti- ties that had traditionally been difficult to tease apart (13). How- Author contributions: V.W., A.C.N., and C.S. designed research; V.W. performed research; ever, SDT has remained largely silent about the computational V.W. contributed new reagents/analytic tools; V.W. and C.S. analyzed data; and V.W., mechanisms by which sensitivity and bias are influenced by con- A.C.N., and C.S. wrote the paper. textual information such as the prior probability and relevance of The authors declare no conflict of interest. the signal. Indeed, changes in signal-to-noise sensitivity can occur This article is a PNAS Direct Submission. either by amplifying the responses of signal-selective units (14) or 1To whom correspondence should be addressed. E-mail: [email protected]. by suppressing performance-limiting noise without amplifying the This article contains supporting information online at www.pnas.org/lookup/suppl/doi:10. signal per se (15). Similarly, changes in bias can arise either by 1073/pnas.1120118109/-/DCSupplemental. www.pnas.org/cgi/doi/10.1073/pnas.1120118109 PNAS Early Edition | 1of6 Fig. 1. Task structure and conventional signal detection analyses. (A) Task structure. Subjects viewed two simultaneously presented stimuli in colored placeholders located in their left and right visual fields. Their task was to report whether a signal was present or absent in one of the two placeholders, indicated by a color-matched probe. We manipulated signal probability at the block level using a cue indicating the prior probability of signal occurrence in each of the two colored placeholders, and signal relevance at the trial level using a prestimulus cue indicating the most likely color of the poststimulus probe. (B) Signal probability biases detection judgments by increasing hit and false-alarm rates to a similar extent. (C) Signal relevance improves the precision of signal processing by selectively decreasing the false-alarm rate for cued stimuli. *P < 0.05; **P < 0.01; ns, nonsignificant effect. Error bars indicate SEM.

− level using a cue indicating the prior probability of signal oc- within S+ and S stimulus categories using binomial parametric currence in each of the two colored placeholders (0.67/0.33, 0.50/ regression (Methods). The regressed energy sensitivity provides an 0.50, or 0.33/0.67), and signal relevance at the trial level using estimate of the strength of the relationship between the amount a prestimulus cue indicating the most likely color of the post- of signal-like energy present in each stimulus and the internal stimulus probe (0.67/0.33, 0.50/0.50, or 0.33/0.67). Signal occur- response upon which detection judgments are made. In contrast rence in the probed placeholder was made independent from the to d′, this measure of sensitivity capitalizes exclusively on the other placeholder (i.e., signals could occur in both, one, or nei- influence of within-category fluctuations in signal energy on ther of the placeholders). This feature ensured that the relevance choice (i.e., precisely the trial-to-trial variability being discarded of the signal (i.e., the fact that its correct detection would yield by conventional analyses). a positive reward) did not depend on its presence in any of the Before assessing the influences of signal probability and rele- two placeholders but on its presence in the placeholder that was vance on energy sensitivity, we first verified that parametric probed afterward. Consequently, the relevance cue did not fluctuations in stimulus energy within each stimulus category (S+ − provide any prior information about whether or where a signal or S ) predicted trial-to-trial variability in signal detection, over was likely to occur. So unlike typical cueing studies based on the and above between-category differences in signal strength (Fig. Posner paradigm (22), the two types of cues provided mutually 2). We first plotted energy sensitivity across varying orientations independent information about signal probability and relevance. and spatial frequencies centered around the attributes of the A Conventional Signal Detection Analyses. target signal (Fig. 2 ) and found that detection judgments were When we estimated sensi- maximally sensitive to signal-like fluctuations in stimulus energy tivity d′ and bias c using conventional methods (1, 2), we repli- in the probed stimulus (t test against zero, t = 12.3, P < 0.001). cated previous studies in that signal relevance increased sensitivity 9 Importantly, this was not the case for the other, unprobed d′ (repeated-measures ANOVA, F = 23.4, P < 0.001), whereas − 2,18 stimulus (t = −0.7, P > 0.5). When considering S+ and S signal probability lowered bias c (F = 10.2, P = 0.001) but did 9 2,18 stimulus categories independently, we found that both hits and not increase d′ (F < 1, P > 0.5) (Fig. 1 B and C and Fig. S1). 2,18 false alarms were sensitive to fluctuations in signal energy binned Sensitivity d′ increased for stimuli cued as relevant (F1,9 = 19.8, P F into quartiles (Fig. 2B and Fig. S2). Indeed, hits increased by = 0.001) and decreased for stimuli cued as irrelevant ( 1,9 = ± F P < P < 27.9% 2.2% ( 1,9 = 167.2, 0.001) and false alarms by 15.5, 0.005) relative to neutral ones, thereby matching known ± F P < fi effects of spatial attention on visual contrast sensitivity (4). By 10.0% 2.4% ( 1,9 = 17.3, 0.005) between the rst and contrast, stimuli cued as likely to contain the signal were associ- fourth energy quartiles. In other words, both hit and false-alarm rates increased parametrically with signal energy, a finding pre- ated with an increased false-alarm rate (F1,9 = 10.0, P = 0.01) (i.e., a more liberal decision criterion according to signal de- dicted by signal detection theory but unaccounted for when using tection theory) (11). conventional analyses. This regression-based approach can also be used to recover Reverse-Correlation Analyses. Rather than classifying stimuli in conventional estimates of sensitivity d′ and bias c, by simply − a binary fashion as signal-present (S+) or signal-absent (S ), we substituting the within-category fluctuations in signal energy with + − then assessed whether trial-to-trial fluctuations in external noise ones and zeros for S and S stimuli, respectively. This allowed us could further account for variability in signal detection. To do so, to compare the conventional (binary) and reverse-correlation we first processed each stimulus through a pool of Gabor energy (parametric) approaches head-to-head and ask which could ac- filters of varying preferred orientations and spatial frequencies count better for trial-to-trial variability in choice (SI Methods). (Methods). The energy response of each filter corresponds to the We found that the reverse-correlation approach was a better contrast of the stimulus with respect to its preferred orientation predictor of choice, as measured by the area under the receiver and spatial frequency. We then estimated the sensitivity of de- operating characteristic curve (conventional: 0.684 ± 0.012; re- tection judgments to trial-to-trial fluctuations in stimulus energy verse-correlation: 0.721 ± 0.013; paired t test, t9 = 9.8, P < 0.001).

2of6 | www.pnas.org/cgi/doi/10.1073/pnas.1120118109 Wyart et al. Fig. 2. Reverse-correlation analyses. (A) Left: Energy sensitivity maps for probed and unprobed stimuli. Subjects’ choices are sensitive to signal-like fluctuations in stimulus energy in the probed stimulus (Left), not in the other stimulus (Right). The highlighted cluster is significant at P < 0.01 corrected for multiple comparisons. Right: Energy sensitivity profile for the probed stimulus. The black line indicates significance at P < 0.05. The shaded area indicates SEM. (B)Hit rate (Left) and false-alarm rate (Right) both increase parametrically with signal energy in the probed stimulus. **P < 0.01; ***P < 0.001. Error bars indicate SEM.

Although both hits and false alarms were sensitive to signal en- of visual contrast processing (Fig. S5). Importantly, the model relies ergy, we also found that false alarms were significantly less sensitive on the same basic assumptions as signal detection theory, namely, than hits to signal-like fluctuations in stimulus energy (paired t test, that detection judgments are based on the level of a continuous t P < fi 9 = 4.2, 0.005). This nding implies that the internal response internal response R corrupted by additive Gaussian noise (1, 2): upon which detection judgments are made does not grow linearly with signal energy but rather indicates the presence of a soft- R ¼ Γ½EðSjTÞþδþNð0; σÞ; threshold nonlinearity at low signal strength, in accordance with previous psychophysical observations (21) (Methods). where E(S|T) corresponds to the energy of the noisy stimulus S conditional to a target signal T, δ to an additive bias to signal-se- Probability × Relevance Effects on Energy Sensitivity. Turning to our lective units, Γ[ . ] to a soft-threshold nonlinearity capturing the main analyses of interest, we went on to assess the influences of contrast-response function of visual neurons, and σ to the SD of COGNITIVE SCIENCES signal probability and relevance on energy sensitivity (Fig. 3 and the performance-limiting internal noise (Methods). Consistent with PSYCHOLOGICAL AND fl Fig. S3). These analyses were performed using trial-to-trial uc- signal detection theory, each decision made by the model is based tuations in signal energy in the probed stimulus only. In contrast on the comparison between the level of the internal response R to conventional analyses, we found that both types of cues in- and an adjustable decision criterion θ (yes if R > θ,nootherwise). creased energy sensitivity, but that they did so in a dissociable Importantly, although changes in δ and θ both influence bias c in fashion. Energy sensitivity was significantly increased at the target conventional terms, a change in δ corresponds to an early shift of orientation for the stimulus cued as signal-present relative to the stimulus cued as signal-absent (F1,9 = 10.5, P = 0.01) (Fig. 3A). Furthermore, the separate analyses of signal-present and signal- absent stimuli revealed that probability increased the energy sensitivity of false alarms (interaction: F1,9 = 5.2, P < 0.05; cued as signal-present: F1,9 = 16.4, P < 0.005; cued as signal-absent: F1,9 = 1.4, P > 0.2) but not of hits (interaction: F1,9 < 1, P > 0.5) (Fig. 3B). In other words, a greater probability of signal occurrence increased not only the global frequency of false positives but also their sensitivity to signal-like fluctuations in stimulus energy. To ensure that this effect of probability cues was not due to a spurious interaction with relevance cues, we ran a control task on another group of subjects for which we manipulated exclusively signal probability, in the same fashion as in the main task, and obtained the same pattern of results (Fig. S4 and SI Results). As expected from the effect of signal relevance on d′, the peak of the energy sensitivity profile at the vertical orientation was also significantly higher for the stimulus cued as relevant (F1,9 = 18.6, P = 0.001) (Fig. 3C). However, unlike probability, relevance increased the energy sensitivity of hits (interaction: F1,9 = 16.5, P < 0.005; cued as relevant: F1,9 = 180.7, P < 0.001; cued as irrelevant: F1,9 = 6.5, P < 0.05) but not of false alarms (interaction: F1,9 = 1.7, P > 0.2) (Fig. 3D). Therefore, although the global frequency of hits did not differ between cued and uncued stimuli (F1,9 < 1, P > 0.5), their sensitivity to signal-like fluctuations in stimulus energy was significantly increased for the stimulus cued as relevant. These dissociable effects of probability and relevance cues Fig. 3. Dissociable effects of signal probability and relevance on energy fi on energy sensitivity can be summarized by the interaction be- sensitivity. (A) Signal probability increases the energy sensitivity pro le at tween four factors—cue type, cue content, stimulus category, and the target orientation. (B) Signal probability increases the sensitivity of false signal energy— F P < alarms, not hits, to parametric changes in signal energy. (C) Like probability, on detection rate ( 1,9 = 5.3, 0.05). signal relevance increases the energy sensitivity profile at the target orientation. (D) Unlike probability, signal relevance increases primarily the sen- Computational Modeling of Probability × Relevance Effects. To ac- sitivity of hits to parametric changes in signal energy. Black lines indicate count for these findings, we described the effects of signal proba- significant effects at P < 0.05. *P < 0.05; **P < 0.01; ***P < 0.001. Shaded bility and relevance on signal detection using a computational model areas and error bars indicate SEM.

Wyart et al. PNAS Early Edition | 3of6 the contrast-response function of signal-selective units, upstream from internal noise, whereas a change in θ corresponds to a late shift in response criterion, downstream from internal noise. We used maximum-likelihood estimation to fit the hit and false-alarm rates predicted by each model at the first and fourth energy quartiles for stimuli cued as signal-present vs. signal-absent, and for stimuli cued as relevant vs. irrelevant (Methods). We compared the quality of the best fits for three competing models with respect to a fourth control model: (i) a model in which δ was allowed to vary between cueing conditions but all other parameters were fixed (“input bias” model), (ii) a model in which only θ could vary (“response bias” model), (iii) a model in which only σ was free (“response gain” model), and (iv) a control model in which all parameters were fixed between cueing conditions (“null” model). We began by testing the ability of each model to capture the changes in hit and false-alarm rates between stimuli cued as signal-present vs. signal-absent. The effects of signal probability were best accounted for by the input bias model, that is, by increasing the additive bias δ for the stimulus cued as signal- present and decreasing it for the stimulus cued as signal-absent (cued as signal-present: +3.6%; cued as signal-absent: −1.6%; likelihood-ratio test against null model, χ2 = 20.5, df = 1, P < 0.001) (Fig. 4A). Importantly, the input bias model captured the observed effects of signal probability both on bias c (F test between data and input bias model, F1,9 < 1, P > 0.5) and on energy sensitivity (F1,9 < 1, P > 0.5). Although the response bias model also vastly outperformed the null model (χ2 = 19.0, df = 1, P < 0.001), it could not capture the effect of signal probability on energy sensitivity, indicating that the response bias model can be formally rejected (F test between data and response bias model, F1,9 = 12.5, P < 0.01) (Fig. 4B). The response gain model did not 2 perform better than the null model (χ = 0.2, df = 1, P > 0.5). Fig. 4. Computational modeling of the effects of signal probability and No combination of the three models outperformed the winning relevance. (A) Input bias model. The input bias model predicts successfully input bias model (SI Methods). the effects of signal probability on bias c and on energy sensitivity. (B) Re- By contrast, the model that best captured the changes in hit and sponse bias model. The response bias model does not predict the effect of false-alarm rates between stimuli cued as relevant vs. irrelevant signal probability on energy sensitivity. (C) Response gain model. The response gain model predicts quantitatively the effects of signal relevance on was the response gain model (likelihood-ratio test against null ′ χ2 P < C σ sensitivity d and on energy sensitivity. Points correspond to observations, model, = 14.7, df = 1, 0.001) (Fig. 4 ). The amount of lines to best-fitting models (Left), and bars to model predictions (Right). internal noise estimated by the model was suppressed by more Model predictions vs. observed effects: *P < 0.05; **P < 0.01. Error bars in- than half between the cued stimulus and the uncued one (cued as dicate SEM. relevant: 8.6%; cued as irrelevant: 18.3%). This response gain model captured the observed effects of signal relevance on sensi- “ ” tivity d′ (F test between data and response gain model, F1,9 < 1, P > statistical regularities of the environment, and attending to fi 0.5) and on energy sensitivity (F1,9 < 1, P > 0.5). Unsurprisingly, that signal on the basis of its behavioral signi cance (23). In neither the input bias model nor the response bias model out- everyday life, these two functions can, and often are, deployed in performed the null model (both P > 0.5). As for signal probability, an orthogonal fashion. For example, some events may be moti- no combination of the three models outperformed the winning vationally highly salient (e.g., cues that are associated with response gain model (SI Methods). impending rewards, or punishments, and demand attention to be deployed to them). However, events also differ with regard to Discussion their probability of occurrence, independent of whether they are We designed a signal detection task that allowed us to dissociate relevant to the current task set. the prior influences of signal probability and relevance on visual The reverse-correlation technique used here constitutes a re- contrast sensitivity. Using a reverse-correlation approach that finement of conventional SDT analysis with no alteration to its quantifies how noise-driven fluctuations in signal energy predict basic assumptions: both approaches assume that detection judg- the trial-to-trial variability in choice unexplained by conventional ments are based on the comparison between a continuous internal SDT analyses, we reveal that signal probability and relevance response and an adjustable decision criterion (1, 2). In fact, our both influence energy sensitivity, albeit in a dissociable fashion: regression-based approach allows to verify empirically one of the relevance increases energy sensitivity primarily for signal-present main predictions of SDT: that hit and false-alarm rates both in- stimuli, whereas probability increases energy sensitivity only for crease parametrically with signal energy. In this respect, the finding signal-absent stimuli. These separable effects can be accounted that false alarms are not pure strategic guesses constitutes in itself for using a computational model in which (i) relevance increases a validation of SDT and allows the ruling out of other, finite-state the signal-to-noise precision of signal processing by suppressing models of detection, such as the high-threshold model (24). internal noise, and (ii) probability biases signal detection by in- Characterizing the mechanisms by which attention enhances creasing the baseline activity of signal-selective units. sensory processing at the behavioral and neuronal levels is a key The computational dissociation between these two types of goal of the neurosciences, and a large body of literature has used prior information maps broadly onto the theoretical difference signal detection theory to measure increases in contrast sensitivity between “expecting” a particular signal to occur because of the when a relevant stimulus is presented at an expected location

4of6 | www.pnas.org/cgi/doi/10.1073/pnas.1120118109 Wyart et al. relative to an unexpected one (3–10). Most, if not all, of these internal noise, whereas signals cued as probable are biased posi- studies have manipulated top-down attention using spatial cues tively by increasing the baseline activity of signal-selective units. that predict the occurrence of a target stimulus at a particular While offering psychophysical evidence for separable top-down location (22). However, such cues provide mixed information influences of expectation and attention on bottom-up sensory about the forthcoming stimulus. First, relative to uninformative processing, these findings also call into question an assumption cues, these predictive cues reduce uncertainty about where the that has endured for more than 50 years, namely, that prior target stimulus is likely to appear. Whether their facilitatory probability biases signal detection only at late response stages. effects on detection sensitivity can be attributed to uncertainty reduction alone is still a matter of debate (25–27) [i.e., by Methods weighting differently the sensory evidence available at cued and Subjects. Ten human subjects aged 19–28 y (six female) participated in the uncued locations in the decision process (28, 29)]. Here we used study after giving informed written consent. All had normal or corrected-to- a poststimulus probe specifically to suppress uncertainty about normal vision, and all were naïve to the purpose of the experiment. Subjects which stimulus was relevant before each choice. Second, most were paid £45 for their participation. previous studies have used a single cue to concurrently (i) indicate Psychophysical Procedures. an increase in the conditional probability that a signal would occur Each of the stimuli consisted of a Gabor pattern (the ii target signal) that could be added to a Gaussian noise patch. The diameter of at the cued location, and ( ) mark the cued location as potentially the stimuli was 4° of visual angle, and their center was positioned at 4° of relevant for subsequent behavior (30). By contrast, we manipu- visual angle to the left and right of fixation. The orientation of the Gabor lated these two types of prior information orthogonally using two patterns was always vertical, their spatial frequency was fixed at two cycles cues and showed that they produce dissociable effects on visual per degree of visual angle (cpd), and their phase was sampled from a uniform contrast processing. random distribution. The noise patch was created by smoothing pixel-by-pixel Our study is not the first to investigate the mechanisms of visual Gaussian noise through a 2D Gaussian smoothing filter. The dimension of the attention using computational modeling (5, 6, 28, 29). Here, our smoothing filter was chosen to maximize the trial-to-trial variability of the reverse-correlation analysis indicates that the facilitatory in- convolution between the smoothed noise and the target signal (i.e., to fl fluence of signal relevance on sensitivity grows with signal maximize the in uence of the noise on the detectability of the signal). Both strength: it is weak for signal-absent stimuli and stronger for this smoothing dimension (0.083° of visual angle) and the contrast of the noise (SD of 10%) were fixed across subjects and stimuli. Further information about signal-present stimuli. Our model demonstrates that this pattern the psychophysical procedures is presented in SI Methods. of results can be best accounted for as a suppression of internal noise during signal processing, without any change in the mean Reverse-Correlation Procedures. Each stimulus was processed through a pool COGNITIVE SCIENCES activity of signal-selective units. This multiplicative mechanism is of Gabor energy filters with varying preferred orientations and spatial fre- PSYCHOLOGICAL AND highly consistent with recent results from electrophysiological quencies using the following equation: recordings in monkey visual cortex (9, 10), which have revealed qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi that most of the facilitatory effects of spatial attention on visual EðSjTÞ¼ ÆS ∗ cosðTÞæ2þÆS ∗ sinðTÞæ2; processing can be explained by a suppression in pair-wise neuronal correlations rather than by an increase in firing rates. where E(S|T) corresponds to the energy of the stimulus S conditional to the Signal probability has been much less studied in the absence of preferred signal T (uniquely defined by its orientation and its spatial fre- spatial uncertainty (25–27) but has classically been thought to quency), and < * > corresponds to the cross-correlation operator. Intuitively, increase hit and false-alarm rates to a similar extent. This finding the response of each energy filter corresponds to the effective contrast of has been interpreted as an idiosyncratic bias occurring at late the stimulus with respect to its preferred signal. fi response stages, unrelated to visual signal processing per se (11, We submitted these single-trial energy lter responses and the corre- sponding detection judgments to binomial regression to estimate energy 12). In contrast to this view, we show that probability increases — fl fl shrinks sensitivity the strength of the relationship between within-category uc- energy sensitivity and that its in uence with signal tuations in signal-like energy and the internal response upon which de- strength (i.e., strongest for signal-absent stimuli). By comparing tection judgments are made. Mathematically, the generalized linear model two models in which probability facilitates signal detection either used for the regression is: at the input stage or at the response stage (31, 32), we confirm ð Þ¼Φ½β þ β · ½ ð j Þ; that only an early influence on signal processing can account for P yes 0 1 Z E S T its observed effects. This distinction is not possible using con- where E(S|T) corresponds to the energy of the stimulus S with respect to the ventional analyses that can only assess the frequency of false fl template signal T, Z[ . ] to the normal deviate function (mean of the stimulus alarms, not their sensitivity to signal-like uctuations in noise. category of S, SD of the signal-absent energy distribution), and Φ[.]tothe At the computational level, the finding that prior probability can cumulative normal function. As for conventional signal detection theory (1, 2), bias the baseline activity of signal-selective units during early visual two parameters are fitted simultaneously: (i) β0 is independent from the processing is in agreement with “predictive-coding” models of stimulus S and corresponds to the normal deviate of the overall detection rate β perception (33–35). This theory of brain function argues that (e.g., the false-alarm rate for signal-absent stimuli), and (ii) 1 indexes the probabilistic expectations about future sensory events flow back- strength of the parametric relationship between E(S|T) and the internal reward from higher associative regions to supplement or “complete” sponse upon which detection judgments are made (i.e., their energy sensi- bottom-up sensory signals. This top-down mechanism allows for tivity). Further information about the reverse-correlation procedures is presented in SI Methods. optimal perceptual inference by minimizing the amount of surprise (or prediction error) left to be encoded by bottom-up signals (36) Modeling Procedures. The equation for the soft-threshold nonlinearity is: and is mathematically equivalent to computational descriptions of – fl how attention biases visual processing (37 39). The early in uence Γ½ ¼ þ − x ; of signal probability is also supported by functional imaging studies x x exp α showing increases in blood oxygen level-dependent (BOLD) sig- α nals for expected stimuli in ventral visual cortex (40, 41) and where x corresponds to the input contrast/energy level, and corresponds to stronger BOLD responses to false alarms relative to misses or the soft threshold, expressed in contrast units. The soft-threshold nonlinearity becomes linear at high contrast levels (>α) and saturates at low correct rejections in primary visual cortex (42). contrast levels (<α). We fitted α to match the within-subject difference in To conclude, we demonstrated that the prior probability and energy sensitivity between hits and false alarms using maximum-likelihood relevance of a visual signal can modulate visual contrast processing estimation. The best-fitting α estimate (11.2%) was fixed across conditions in a dissociable manner. Visual signals cued as relevant are pro- for all computational simulations reported in the manuscript. This static cessed with an increased signal-to-noise precision by suppressing nonlinearity, commonly used in computational studies of visual contrast

Wyart et al. PNAS Early Edition | 5of6 processing (5, 6), captures the contrast-response function of noisy pop- This scheme ensures that between-subject variability in overall detection ulation responses at low contrast levels. Further information about the performance is appropriately controlled for and cannot account for signiﬁ- modeling procedures is presented in SI Methods. cant group-level effects. Further information about the statistical procedures is presented in SI Methods. Statistical Procedures. All analyses were performed at the single-subject level (see Fig. S6 and Fig. S7 for a representative subject) and followed by stan- ACKNOWLEDGMENTS. We thank Vincent de Gardelle, Gustavo Rohenkohl, dard parametric tests at the group level (e.g., paired t tests, repeated- Mark Stokes, and two anonymous reviewers for useful suggestions and measures ANOVAs) to assess reliable within-subject differences between comments. This work is supported by a postdoctoral research grant from the cueing conditions (signal-present vs. signal-absent, relevant vs. irrelevant). Fyssen Foundation (to V.W.).

1. Green DM, Swets JA (1966) Signal Detection Theory and Psychophysics (John Wiley & 23. Summerfield C, Egner T (2009) Expectation (and attention) in visual cognition. Trends Sons, New York). Cogn Sci 13:403–409. 2. Macmillan NA, Creelman CD (2005) Detection Theory: A User’s Guide (Lawrence Erl- 24. Blackwell HR (1963) Neural theories of simple visual discriminations. J Opt Soc Am 53: baum Associates, London), 2nd Ed. 129–160. 3. Bashinski HS, Bacharach VR (1980) Enhancement of perceptual sensitivity as the result 25. Palmer J, Ames CT, Lindsey DT (1993) Measuring the effect of attention on simple of selectively attending to spatial locations. Percept Psychophys 28:241–248. visual search. J Exp Psychol Hum Percept Perform 19:108–130. 4. Carrasco M (2006) Covert attention increases contrast sensitivity: Psychophysical, 26. Solomon JA, Lavie N, Morgan MJ (1997) Contrast discrimination function: spatial neurophysiological and neuroimaging studies. Prog Brain Res 154:33–70. cuing effects. J Opt Soc Am A Opt Image Sci Vis 14:2443–2448. 5. Lu ZL, Dosher BA (2008) Characterizing observers using external noise and observer 27. Gould IC, Wolfgang BJ, Smith PL (2007) Spatial uncertainty explains exogenous and models: Assessing internal representations with external noise. Psychol Rev 115: endogenous attentional cuing effects in visual signal detection. JVis7:4.1–17. 44–82. 28. Verghese P (2001) Visual search and attention: A signal detection theory approach. 6. Smith PL, Ratcliff R (2009) An integrated theory of attention and decision making in Neuron 31:523–535. visual signal detection. Psychol Rev 116:283–317. 29. Eckstein MP, Peterson MF, Pham BT, Droll JA (2009) Statistical decision theory to re- 7. McAdams CJ, Maunsell JH (1999) Effects of attention on the reliability of individual late neurons to behavior in the study of covert visual attention. Vision Res 49: neurons in monkey visual cortex. Neuron 23:765–773. 1097–1128. 8. Reynolds JH, Pasternak T, Desimone R (2000) Attention increases sensitivity of V4 30. Ciaramitaro VM, Cameron EL, Glimcher PW (2001) Stimulus probability directs spatial neurons. Neuron 26:703–714. attention: An enhancement of sensitivity in humans and monkeys. Vision Res 41: 9. Mitchell JF, Sundberg KA, Reynolds JH (2009) Spatial attention decorrelates intrinsic 57–75. activity fluctuations in macaque area V4. Neuron 63:879–888. 31. Carpenter RH, Williams ML (1995) Neural computation of log likelihood in control of 10. Cohen MR, Maunsell JH (2009) Attention improves performance primarily by reducing saccadic eye movements. Nature 377:59–62. interneuronal correlations. Nat Neurosci 12:1594–1600. 32. Platt ML, Glimcher PW (1999) Neural correlates of decision variables in parietal cortex. 11. Swets JA, Tanner WP, Jr., Birdsall TG (1961) Decision processes in perception. Psychol Nature 400:233–238. Rev 68:301–340. 33. Mumford D (1992) On the computational architecture of the neocortex. II. The role of 12. Terman M, Terman JS (1972) Concurrent variation of response bias and sensitivity in cortico-cortical loops. Biol Cybern 66:241–251. an operant-psychophysical test. Percept Psychophys 11:428–432. 34. Rao RP, Ballard DH (1999) Predictive coding in the visual cortex: A functional in- 13. Swets JA (1996) Signal Detection Theory and ROC Analysis in Psychology and Diag- terpretation of some extra-classical receptive-field effects. Nat Neurosci 2:79–87. nostics (Lawrence Erlbaum Associates, London). 35. Friston K (2005) A theory of cortical responses. Philos Trans R Soc Lond B Biol Sci 360: 14. Yeshurun Y, Carrasco M (1998) Attention improves or impairs visual performance by 815–836. enhancing spatial resolution. Nature 396:72–75. 36. Friston K (2010) The free-energy principle: A unified brain theory? Nat Rev Neurosci 15. Dosher BA, Lu ZL (2000) Noise exclusion in spatial attention. Psychol Sci 11:139–146. 11:127–138. 16. Liston DB, Stone LS (2008) Effects of prior information and reward on oculomotor and 37. Desimone R, Duncan J (1995) Neural mechanisms of selective visual attention. Annu perceptual choices. J Neurosci 28:13866–13875. Rev Neurosci 18:193–222. 17. Reynolds JH, Heeger DJ (2009) The normalization model of attention. Neuron 61: 38. Reynolds JH, Chelazzi L (2004) Attentional modulation of visual processing. Annu Rev 168–185. Neurosci 27:611–647. 18. Eckstein MP, Shimozaki SS, Abbey CK (2002) The footprints of visual attention in the 39. Spratling MW (2008) Predictive coding as a model of biased competition in visual Posner cueing paradigm revealed by classification images. JVis2:25–45. attention. Vision Res 48:1391–1408. 19. Murray RF (2011) Classification images: A review. JVis11:11. 40. Stokes M, Thompson R, Nobre AC, Duncan J (2009) Shape-specific preparatory activity 20. Hubel DH, Wiesel TN (1959) Receptive fields of single neurones in the cat’s striate mediates attention to targets in human visual cortex. Proc Natl Acad Sci USA 106: cortex. J Physiol 148:574–591. 19569–19574. 21. Lee DK, Itti L, Koch C, Braun J (1999) Attention activates winner-take-all competition 41. Egner T, Monti JM, Summerfield C (2010) Expectation and surprise determine neural among visual filters. Nat Neurosci 2:375–381. population responses in the ventral visual stream. J Neurosci 30:16601–16608. 22. Posner MI, Snyder CR, Davidson BJ (1980) Attention and the detection of signals. J Exp 42. Ress D, Heeger DJ (2003) Neuronal correlates of perception in early visual cortex. Nat Psychol 109:160–174. Neurosci 6:414–420.

6of6 | www.pnas.org/cgi/doi/10.1073/pnas.1120118109 Wyart et al.